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All truths are easy to understand once they are discovered; the point is to discover them. Galileo GalileiExperimental data on internal homogeneous crystal nucleation in silicate glasses obtained in the last four decades are analyzed in detail in the framework of the classical nucleation theory (CNT). Despite the fact that reasonable qualitative interpretations of the temperature and time dependences of nucleation rates are given by CNT, it meets with serious problems in their quantitative description. Different reasons for this failure are tested and discussed. The main conclusion is that, in contrast to Gibbs' description of heterogeneous systems, the thermodynamic properties of critical nuclei which, to a large extent, govern nucleation kinetics, generally differ from those of the corresponding macrophase. A number of evidences based on the analysis of both crystal nucleation and growth data are given for a decreased thermodynamic driving force for crystallization and critical nuclei/liquid interfacial energy, as compared with the respective properties of the macro-phase. Special attention is devoted to the widespread and practically important type of heterogeneous nucleation -nucleation on glass surfaces. A comparative analysis of available data on surface and bulk nucleation rate data is performed. IntroductionGlasses can be defined as noncrystalline solids that, in the course of their preparation, undergo a process commonly denoted as glass transition. One of the most important (but not the only) ways of vitrification consists in supercooling a liquid suppressing crystallization. When a liquid is cooled down with sufficiently high rates, crystallization may occur to a very limited degree or be completely absent down to temperatures corresponding to very high viscosities in the range η ≥ 10 13 -10 12 Pa · s ∼ = η(T g ), where T g is defined as the glass transition temperature. Below this temperature, the viscosity is so high that large-scale atomic rearrangements in the system are no longer possible within the time-scale of the experiment, and the structure freezes-in, i.e., the structural rearrangements required to retain the liquid in the appropriate metastable equilibrium state cannot follow any more the changes of temperature. This process of freezing-in of the structure of an undercooled liquid is commonly denoted as glass transition and, as a result, the system is transformed into a glass. Typical glass-forming liquids, such as silicate melts, are commonly characterized by: (i) relatively high viscosities (η > 100 Pa · s) at the melting point (or liquidus), and (ii) a steep increase of the viscosity with decreasing temperature. These properties favor the process of transformation of a liquid into a glass. The above mechanism discussed leads to the conclusion that the glass structure is very similar to that of the parent (undercooled) liquid at temperatures near T g .